be the relation on 
(i.e., the set of nonzero integers) defined by 
if 
For each of the five properties of relations, determine if this relation
has the property and prove your assertion (with either a proof or a counterexample
as appropriate.) Note: Make sure your work is done in an organized and
neat fashion. It will not receive credit if it is not easily and clearly
understandable.
Give an example of a relation 
on 
that is transitive, but neither symmetric nor reflexive.